### Abstract

By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to this end, in which the numerical results are compared with corresponding values obtained using the finite element method (FEM). An assessment of the relative efficiency of the BEM analysis when using the present exact form of the derivatives versus another previous exact form is also presented.

Original language | English |
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Pages (from-to) | 95-108 |

Number of pages | 14 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 78 |

Issue number | 2 |

Publication status | Published - 2011 Nov 29 |

### All Science Journal Classification (ASJC) codes

- Software
- Modelling and Simulation
- Computer Science Applications